Q 11-04-012JEE MainEAMCET 2014 (Engineering)Medium
A body of mass $8$ kg is moved by a force $F = (3x)$ N, where $x$ is the distance covered. Its initial position is $x = 2$ m and its final position is $x = 10$ m. If the body is initially at rest, its final speed is
Answer: (C) $6\ \text{m/s}$
Concept. Work–energy: $\displaystyle\int F\,dx = \Delta K$.
Step 1. Work. $\displaystyle\int_2^{10}3x\,dx = \frac32(100 - 4) = 144$ J.
Step 2. Speed. $\dfrac12 \times 8v^2 = 144 \Rightarrow v = 6$ m/s.
Answer. $6\ \text{m/s}$ (Option C).
Solution by Sreeraj P, M.Sc Physics